An optimized high-order hybrid implicit and explicit spatiotemporal finite-difference scheme for acoustic wavefield extrapolation
Zhangyongrui Gao, Hongwei Liu, Zhendong Zhang, Yike Liu · Geophysics · 2025
ABSTRACT Seismic forward modeling is critical for seismic data processing, and the development of an efficient and accurate wavefield extrapolation algorithm is ongoing. Explicit finite-difference (FD) schemes, which are derived from the Taylor expansion, often cannot adequately balance computational cost and simulation accuracy and are known to suffer from saturation effects. Here, we provide a spatial implicit FD scheme with optimal coefficients that only requires approximately one-third of the computational cost of the 64th-order explicit FD scheme, yet achieves the same accuracy. In particular, we use the Z-transform to derive the implicit form of a high-order FD scheme for spatial derivatives. Causal-and-acausal integration is used to compute the spatial FD. The Lax-Wendroff temporal stepping strategy is also used to avoid potential temporal dispersion and the inherent instability of high-order temporal differentiation. In addition, we compute the optimal FD coefficients using the Remez exchange algorithm to improve the accuracy of the FD schemes further. We verify the effectiveness and accuracy of our scheme using a homogeneous model and two reference models. The results demonstrate that the new FD scheme allows for a larger time step, achieving similar accuracy while reducing computational costs by two-thirds compared with the 64th-order explicit FD scheme.